Razumikhin-type theorem for stochastic functional differential systems via vector Lyapunov function

Liu, Lie and Mao, Xuerong and Cao, Jinde (2019) Razumikhin-type theorem for stochastic functional differential systems via vector Lyapunov function. Journal of Mathematical Analysis and Applications, 479 (2). pp. 1986-2006. ISSN 0022-247X

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Official URL: https://doi.org/10.1016/j.jmaa.2019.07.037

Abstract

This paper is concerned with input-to-state stability of SFDSs. By using stochastic analysis techniques, Razumikhin techniques and vector Lyapunov function method, vector Razumikhin-type theorem has been established on input-to-state stability for SFDSs. Novel sufficient criteria on the pth moment exponential input-to-state stability are obtained by the established vector Razumikhin-type theorem. When input is zero, an improved criterion on exponential stability is obtained. Two examples are provided to demonstrate validity of the obtained results.

Author(s):	Liu, Lie, Mao, Xuerong ORCID: https://orcid.org/0000-0002-6768-9864 and Cao, Jinde
Item type:	Article
ID code:	69222
Keywords:	vector Lyapunov function, razumikhin-type theorems, input-to-state stability, exponential stability, stochastic functional differential equation, Probabilities. Mathematical statistics, Mathematics(all)
Subjects:	Science > Mathematics > Probabilities. Mathematical statistics
Department:	Faculty of Science > Mathematics and Statistics
Depositing user:	Pure Administrator
Date deposited:	06 Aug 2019 10:01
Last modified:	15 Nov 2019 06:04
Related URLs:	Journal or Publication
URI:	https://strathprints.strath.ac.uk/id/eprint/69222
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